Find the value of $x$ for which the points $(x, -1), (2, 1),$ and $(4, 5)$ are collinear.

$A$ line passes through $(2,2)$ and is perpendicular to the line $3x+y=3$. Its $y$-intercept is:

The equations of the lines which pass through the point of intersection of the lines $4x - 3y - 1 = 0$ and $2x - 5y + 3 = 0$ and are equally inclined to the axes are

The Fahrenheit temperature $F$ and absolute temperature $K$ satisfy a linear equation. Given that $K=273$ when $F=32$ and that $K=373$ when $F=212$. Express $K$ in terms of $F$ and find the value of $F$,when $K =0$.

If $p$ and $q$ are the $x$ and $y$-intercepts respectively of the line passing through the points $(a \cos \alpha, b \sin \alpha)$ and $(a \cos \beta, b \sin \beta)$,then $\frac{a^2}{p^2}+\frac{b^2}{q^2}=$

Find the equation of the line passing through the point $(-2, 3)$ with a slope of $-4$.